Solve (2x+2)^2=(x-3)(x+5)+3x^2

$$( 2 x + 2 ) ^ { 2 } = ( x - 3 ) ( x + 5 ) + 3 x ^ { 2 }$$

Solve for x

$$x = -\frac{19}{6} = -3\frac{1}{6} \approx -3.166666667$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+2\right)^{2}.

$$4x^{2}+8x+4=\left(x-3\right)\left(x+5\right)+3x^{2}$$

Use the distributive property to multiply x-3 by x+5 and combine like terms.

$$4x^{2}+8x+4=x^{2}+2x-15+3x^{2}$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$4x^{2}+8x+4=4x^{2}+2x-15$$

Subtract 4x^{2} from both sides.

$$4x^{2}+8x+4-4x^{2}=2x-15$$

Combine 4x^{2} and -4x^{2} to get 0.

$$8x+4=2x-15$$

Subtract 2x from both sides.

$$8x+4-2x=-15$$

Combine 8x and -2x to get 6x.

$$6x+4=-15$$

Subtract 4 from both sides.

$$6x=-15-4$$

Subtract 4 from -15 to get -19.

$$6x=-19$$

Divide both sides by 6.

$$x=\frac{-19}{6}$$

Fraction \frac{-19}{6} can be rewritten as -\frac{19}{6} by extracting the negative sign.

$$x=-\frac{19}{6}$$